numeric-diff 1.0.0

This Python package containts functions that do numeric differentiation.

FirstSecondNumericDiff

A Python class for computing first and second-order numerical derivatives using finite difference methods.

Features

• Computes first and second derivatives using:
  • Forward Difference
  • Backward Difference
  • Central Difference
• Handles uniformly spaced data.
• Provides warning when handling non-uniformly spaced data.
• Provides error handling for invalid data formats.

Installation

This class requires Python.

Usage

To use this module, import it from the numeric_diff package like this:

from numeric_diff import first_second_numeric_diff

And use it like this:

x_data = [1, 2, 3, 4, 5] y_data = [7.5, 8.3, 9.1, 10.8, 12] order = 'First' method = 'Forward'

x_output, y_output = first_second_numeric_diff(x_data, y_data, order, method)

Methods

init(x_data, y_data, order, method)

Initializes the numerical differentiation class

• Parameters:
  • x_data (list, tuple, set, or NumPy array): Independent variable values.
  • y_data (list, tuple, set, or NumPy array): Dependent variable values.
  • order (str): Numerical differentiation order.
  • method (str): Numerical differentiation method.

__first_second_numeric_differentiation(x_data, y_data, order, method)

Computes the specified derivative.

• Parameters:
  • x_data (list, tuple, set, or NumPy array): Independent variable values.
  • y_data (list, tuple, set, or NumPy array): Dependent variable values.
  • order (str): Numerical differentiation order. Options:
    • 'first': Calculates first-order derivative.
    • 'second': Calculates second-order derivative.
  • method (str): Numerical differentiation method. Options:
    • 'forward': Uses forward difference.
    • 'backward': Uses backward difference.
    • 'central': Uses central difference.

__first_order_differentiation(x_data, y_data, method)

Computes the first derivative.

• Parameters:
  • x_data (list, tuple, set, or NumPy array): Independent variable values.
  • y_data (list, tuple, set, or NumPy array): Dependent variable values.
  • method (str): Numerical differentiation method. Options:
    • 'forward': Uses forward difference.
    • 'backward': Uses backward difference.
    • 'central': Uses central difference.
  • Returns: list of independent variable values and list of first derivative values.

__second_order_differentiation(x_data, y_data, method)

Computes the second derivative.

• Parameters:
  • x_data (list, tuple, set, or NumPy array): Independent variable values.
  • y_data (list, tuple, set, or NumPy array): Dependent variable values.
  • method (str): Numerical differentiation method. Options:
    • 'forward': Uses forward difference.
    • 'backward': Uses backward difference.
    • 'central': Uses central difference.
  • Returns: list of independent variable values and list of second derivative values.

__forward_diff_first_order(x_data, y_data)

Computes the first derivative with forward difference.

• Parameters:
  • x_data (list, tuple, set, or NumPy array): Independent variable values.
  • y_data (list, tuple, set, or NumPy array): Dependent variable values.
• Returns: list of independent variable values and list of first derivative values.

__backward_diff_first_order(x_data, y_data)

Computes the first derivative with backward difference.

• Parameters:
  • x_data (list, tuple, set, or NumPy array): Independent variable values.
  • y_data (list, tuple, set, or NumPy array): Dependent variable values.
• Returns: list of independent variable values and list of first derivative values.

__central_diff_first_order(x_data, y_data)

Computes the first derivative with central difference.

• Parameters:
  • x_data (list, tuple, set, or NumPy array): Independent variable values.
  • y_data (list, tuple, set, or NumPy array): Dependent variable values.
• Returns: list of independent variable values and list of first derivative values.

__forward_diff_second_order(x_data, y_data)

Computes the second derivative with forward difference.

• Parameters:
  • x_data (list, tuple, set, or NumPy array): Independent variable values.
  • y_data (list, tuple, set, or NumPy array): Dependent variable values.
• Returns: list of independent variable values and list of first derivative values.

__backward_diff_second_order(x_data, y_data)

Computes the second derivative with backward difference.

• Parameters:
  • x_data (list, tuple, set, or NumPy array): Independent variable values.
  • y_data (list, tuple, set, or NumPy array): Dependent variable values.
• Returns: list of independent variable values and list of first derivative values.

__central_diff_second_order(x_data, y_data)

Computes the second derivative with central difference.

• Parameters:
  • x_data (list, tuple, set, or NumPy array): Independent variable values.
  • y_data (list, tuple, set, or NumPy array): Dependent variable values.
• Returns: list of independent variable values and list of first derivative values.

Notes

• If x_data type is not valid, an Exception will rise.
• If y_data type is not valid, an Exception will rise.
• If x_data and y_data do not have the same length, an Exception will rise.
• If length of x_data and y_data is less than 2, an Exception will rise.
• If the elements of x_data and y_data are not valid float values, an Exception will rise.
• If order type is not valid, an Exception will rise.
• If method type is not valid, an Exception will rise.
• If length of x_data and y_data is less than 3 for second-order derivative, an Exception will rise.
• If length of x_data and y_data is less than 3 for first-order derivative with central difference, an Exception will rise.

Authors

Juan David Amaya Carreño - [e-mail]